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C. Evaluate the objective function for all the
neighboring points and add these into taboo
list.
D. Find the Pareto-front using the set of points
for which the objective function is evaluated
and update the Pareto list as the current
Pareto-front.
E. Amongst the neighboring points for the cur-
rent iteration choose the one that is on the
Pareto-front and minimizes the cost function
as the next seed point and add this point into
the seed list. If there is no point which satis-
fies these conditions choose randomly one
of the points from the Pareto list amongst
the ones that are not already in the seed list.
F. Check if the predetermined maximum
number of objective function evaluations
is exceeded; if yes stop, if not go to Step b.
for the application. Seven design variables are
defined for the optimization problem as given in
Table 2, alongside the minimum and maximum
values and increments. The combination of these
design variables results in 30000 cases which
constitute the search space. The objectives of
the optimization problem are selected as initial
and life-cycle cost, and structural performance in
terms of maximum interstory drift. No constraints
are defined because of the fact that code-based
seismic design is not performed. The initial cost
of the frames considers only the material costs.
The unit prices for concrete and steel are assumed
to $0.13/liters and $0.66/kg, respectively.
A site at the intersection of 2
nd
and Market
Streets in San Francisco, CA (with coordinates
37° 47´ 21.58´´ N, 122° 24´ 04.77´´ W) is se-
lected and the site-specific seismic hazard is
consistently derived. The soil conditions might
significantly alter the characteristics of the ground
motions at a site, therefore, the soil conditions are
also taken into account in the development of the
hazard curves. The soil at the selected site is
determined as D on the NEHRP (FEMA, 2003)
scale with a shear wave velocity in the range from
180 m/sec to 360 m/sec. Site specific hazard curve
for PGA is shown in Figure 11(a). UHS for three
different return periods (i.e. 75, 475, and 2475
years) are obtained, see Figure 11(b), for record
selection and scaling purposes. These return pe-
riods are mapped onto three structural limit states
IO, LS and CP, respectively. One earthquake
The steps required to perform LCC oriented
seismic design optimization according to the
methodology presented in the preceding sections
is outlined in Figure 9.
EXAMPLE APPLICATION
In this section, the formulations presented in the
preceding sections are applied to a building as an
illustration of the framework on LCC oriented
seismic design optimization. The 2-story 2-bay
RC frame structure show in Figure 10 is selected
Table 2. Design variables and ranges for the considered structural frame
Minimum
Maximum
Increment
Column Reinforcement Ratio
1.0%
2.5%
0.50%
Beam Reinforcement Ratio
0.5%
2.0%
0.50%
Width of Exterior Columns (mm)
660.4
863.9
50.8
Width of Interior Columns (mm)
711.2
914.4
50.8
Depth of Columns (mm)
457.2
660.4
50.8
Width of Beams (mm)
508
711.2
50.8
Depth of Beams (mm)
406.4
508
50.8
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